US 2014/0334621 A1 · Method for Complete Atomic Blocks for Elliptic Curves in Jacobian Coordinates over Prime Fields Countermeasure for Simple-Side Channel Attacks and C-Safe-Fault Attacks for Left-to-Right Algorithms

Abstract

The present invention describes a method which improves the safety aspects of the previously published atomic blocks. This method builds new sets of atomic blocks designed to protect against both simple side-channel attacks and C-safe fault attacks for scalar multiplication for elliptic curves over prime fields. These atomic blocks are structured with the sequence of field operations (S, N, A, A, M, A), Squaring, Negation, Addition, Addition, Multiplication, Addition. These atomic blocks are applied to various operations in Jacobian coordinates: doubling, tripling, and quintupling, as well as mixed Jacobian-affine addition for use in left-to-right scalar multiplication.

Claims13

Dependent claims

Atomic blocks to protect cryptosystems against simple side-channel attacks (SSCA) and C-Safe fault attacks, CHARACTERIZED in that they comprise eliminating the use of dummy operations in the atomic blocks used in the scalar multiplication ([d]P), which are based on elliptic curves defined on fields of prime characteristic, wherein the curves are of the type y2=x3−3x+b with bεGF(p) and the discriminate is Δ=−108+27b2≠0(mod p).

Dependencies are inferred from the claim text.

Facts

Application

13/892,816Filed 13 May 2013

Published

13 Nov 2014

Term ends

Not estimatedThe source records don’t support an estimate.

Classification6 codes

G06F 7/725
Finite field arithmetic: over elliptic curves
H04L 9/003
Countermeasures against attacks on cryptographic mechanisms: for power analysis, e.g. differential power analysis [DPA] or simple power analysis [SPA]
H04L 9/004
Countermeasures against attacks on cryptographic mechanisms: for fault attacks
G06F 2207/7228
Randomisation as countermeasure against side channel attacks: random curve mapping, e.g. mapping to an isomorphous or projective curve

Method for Complete Atomic Blocks for Elliptic Curves in Jacobian Coordinates over Prime Fields Countermeasure for Simple-Side Channel Attacks and C-Safe-Fault Attacks for Left-to-Right Algorithms

Life of this patent

Method for Complete Atomic Blocks for Elliptic Curves in Jacobian Coordinates over Prime Fields Countermeasure for Simple-Side Channel Attacks and C-Safe-Fault Attacks for Left-to-Right Algorithms

Life of this patent

Abstract

Claims13